Photonic integrated beam delivery for a rubidium 3D magneto-optical trap

Cold atoms are important for precision atomic applications including timekeeping and sensing. The 3D magneto-optical trap (3D-MOT), used to produce cold atoms, will benefit from photonic integration to improve reliability and reduce size, weight, and cost. These traps require the delivery of multiple, large area, collimated laser beams to an atomic vacuum cell. Yet, to date, beam delivery using an integrated waveguide approach has remained elusive. Here we report the demonstration of a 87Rb 3D-MOT using a fiber-coupled photonic integrated circuit to deliver all beams to cool and trap > 1 ×106 atoms to near 200 μK. The silicon nitride photonic circuit transforms fiber-coupled 780 nm cooling and repump light via waveguides to three mm-width non-diverging free-space cooling and repump beams directly to the rubidium cell. This planar, CMOS foundry-compatible integrated beam delivery is compatible with other components, such as lasers and modulators, promising system-on-chip solutions for cold atom applications.

Waveguides under microscope 500 um Exposure calibration procedure. To calibrate the lithography steps for the waveguide and grating etches, two sets of focus exposure array jobs with the ASML PAS 5500 stepper tool were done using a wafer with silicon nitride on top of thermal oxide on a silicon substrate. The doses of the center elements were 16 mJ cm -2 and 25 mJ cm -2 , respectively. The focus offset difference between the elements was 0.2 μm for both. An image quality control (IQC) procedure was run on the tool to ensure that the absolute focus exposure correction while running a job would be less than 20 nm. After development of the resist and etching of the antireflective coating layer, the nitride layer was etched with our standard recipes for the waveguide and grating etches 1,2 , as shown in Supplementary Fig. 1. Subsequently, the wafer was cleaned and measurements of the waveguide and grating dimensions were taken with a SEM. The elements of the focus exposure array with the best quality were used to inform the conditions for the PIC devices of this work.

Supplementary Note 3: Beam delivery device design
Supplementary Fig. 2. Beam delivery device design. a) Waveguide dimension for single-mode operation at 780 nm. b) Slab expander and grating emitter. c) Image of the slab expander grating emitter illuminated with 780 nm light. d) Simulation of the slab expander rate of beam expansion. The expander enables reaching an on-chip beam width of 3.5 mm after 4.2 mm of expansion. e) AFM images at three profile locations shows that the grating emitter partial etch depth is relatively uniform across the emitter. f) Simulation of achievable on-chip beam size in the y dimension for different grating partial etch depths.
Grating design and modeling. The laser cooling beams are formed using three large-area, chip-tofree-space grating couplers. These couplers are formed in a material system composed of a silicon nitride device layer and two silicon dioxide cladding layers. Historically, grating couplers have

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been used in integrated photonics for a relatively small subset of tasks, the most well-known of which is likely the coupling of light between chip-scale waveguides and optical fibers 3 . Grating couplers are ideal for interfacing between planar devices and their surrounding environment. Due to the careful control over the grating's k-vector, the angle at which light is either emitted or transmitted can be targeted with a high degree of precision. When light propagating within a chip diffracts from a grating written into its path, the angle at which the light diffracts relative to the chip's surface normal may be calculated analytically. If we assume that the light is initially propagating within the x-y plane, and that the z-axis represents the direction normal to the chip's surface, then the diffraction angle is given as: In these expressions, # and ' are the -andcomponents of the initial k-vector of the light, and # and ' are the -and -components of the grating's k-vector, respectively. Additionally, #,% , ',% , and (,% represent the three components of the diffracted light's k-vector in free-space. For the MOT, the three beams diffracted from the chip are required to each be orthogonal to one another. This requires that for each grating the diffraction angle relative to the surface normal equals 54.7° and the slabs spaced 120° apart from each other. The center of each grating emitter is placed on 13.5 mm circle to ensure the 9.45 mm intersection spot which enables enough clearance for waveplates and cell wall. At the interface between the waveguide, which provides two-dimensional confinement, and the slab expander, which only provides confinement along one axis, the optical wave begins to diverge along the direction which is both transverse to its propagation and parallel to the chip's surface normal. This divergence can be represented mathematically as a spatially dependent distribution of optical k-vectors, given as: In this expression, x and y are the coordinates within the nitride slab relative to the point at which the waveguide-to-slab transition occurs. This means that because the light is required to be emitted in a specific direction regardless of position, the grating coupler's k-vector must vary spatially to compensate for the varying components of the optical k-vector. This requirement may be represented mathematically as: After these local maps of grating period and direction have been calculated, the spatially variant grating may be generated numerically by beginning a single grating line at a chosen starting point and "walking forward", iteratively defining its movement and width. This process may be repeated for an arbitrary number of grating lines until the chosen grating area has been defined. We thus generate curved gratings which take slab mode and produce a flat intensity profile in free space. Based on results from a previous fabrication run we re-used a photolithography mask with a grating length of 5.25 mm (corresponding to a cross-sectional beam width of 2.5 mm). The grating etch depth required for an on-chip beam width of 5.25 mm was simulated to be 12 nm in a 120 nm core. A 10 nm grating etch depth was chosen considering a potential 20% etch depth variation. Subsequent measurements of AFM show that the etch depth variation is smaller than expected (Supplementary Fig. 2(d)). The grating coupling strength is lowest at the grating input and progressively increases as the light propagates in the grating region. The grating period and duty cycle are designed to progress from 1.18 μm -1.08 μm and 10% -50% from front to end of the grating respectively (Supplementary Fig. 2(b)).

Supplementary Note 4: Beam delivery device characterization and future improvements
Optical losses in the beam delivery. We measured the optical losses at each major component on another beam delivery PIC device of the same fabrication run (see Supplementary Table 1). The individual losses of facet, MMI, slab expander and grating were extracted by iteratively measuring and dicing the device in a cutback method. First, the loss of full-size device was measured. Next, the grating was diced from slab and an integrating sphere was used to measure the slab output and extract the grating loss. Finally, waveguide output without the slab was measured to extract the facet coupling loss. The propagation loss was measured by subtracting the facet loss from a long loop around waveguide. For the single grating emitter measured, the total loss from the waveguide input to the grating output beam was 12.5 dB. The MMI splitter excess loss was inferred from the performance of one of the beams of the PIC device used in this work.
The rightmost column of Supplementary Table 1 estimates the achievable losses in future beam delivery PIC designs based on simulations, test structure measurements, and values from literature. The MMI splitter excess losses originate from fabrication imperfections due to the small dimensions of MMI which in the future we will address by replacing the MMI with an evanescent coupler which we have measured to have <0.3 dB loss. The fiber-to-chip coupling loss can be reduced by using tapered mode matchers, facet polishing, or other mode-matching structures 4 . Next, our waveguide is designed to support a TE mode with an estimated loss of ~0.3 dB cm -1 . By increasing the waveguide width we can operate in TM mode which has been shown to achieve a lower loss 5 . We estimate that with a loss of 0.15 dB cm -1 we can achieve a total propagation loss of 0.7 dB. Lastly, the grating emitter output power is distributed over different diffracted orders which affects the overall beam delivery efficiency (Supplementary Figure 3(b)). We define the power in the target diffracted order as * and the power in the other diffracted order (near vertical) as +" and a ratio = +" / * . From simulation we find that we can improve the diffraction efficiency into the 0 order and reduce by adjusting the grating partial etch depth. We find that at an optimal etch depth we can reach = 0.5 (supplementary Figure 3(c)). Assuming that the fraction of total optical power delivered by the emitter is unchanged, we estimate that we can reduce the grating output loss by 1.1 dB. This requires accurate control of the etch depth and with proper calibration a tolerance of <0.5 nm can be achieved. Furthermore, our simulation predicts that for a 10 nm etch depth and a 5.25 mm length grating section, 20% of the power is not diffracted and scatters. By extending the grating length to 7 mm we predict that we can increase the diffracted power and reduce the total grating output loss by 1.7 dB. We estimate a total achievable beam deliver loss (input fiber to all three beams) of 7.2 dB. Further improvements may be possible by using a bottom reflector below the grating 6 and using grating inverse design 7 .  b) Image of the higher-order mode for beams 2 and 3 (B2, B3) with imaging paper sheet above the beam intersection point. The +1 order for the third beam (not shown) has a similar profile. c) Simulation for ratio of power of diffracted orders for varying partial etch depths.
Beam collimation and intensity profile. The beams profile and angle of the intersecting beams was measured with a camera that imaged a translucent paper sheet held above the PIC surface at Input varying distances. The measured beam width (defined as the !& diameter) for beam B1 as a function of the distance from the emitter is shown in Supplementary Fig. 3 (a). We note that beam B3 has a non-uniformity in its intensity profile which we attribute to imperfect photolithography exposure which effectively reduced the width of the waveguide at the input to the slab expander. We attribute the fact that the MOT cloud is not centered inside the beam overlap volume to this beam non-uniformity. By using a focusing lens to collect a portion of the fluorescence power ,-onto a photodetector of responsivity ( ) and transimpedance gain , the output photodetector voltage is When the MOT is switched on (by enabling the magnetic field), the number of atoms will increase according to

Supplementary
where 2%0> is the atom loading time in the trap and * is the steady-state (i.e. maximum) atom number in the MOT. Given a trace of the photodiode voltage during a loading rate measurement, the maximum atom number can be measured: & is recorded at CDE + 70 ms when the MOT has dissipated. The cooling and repump beams are shuttered with the 780 nm semiconductor optical amplifier (SOA) and the probe is shuttered with an AOFS. As the probe beam passes through the cloud, the intensity & of the beam will be attenuated according to Beer's law: Where ( , , ) is the atom number density which can be integrated along the beam axis to obtain the integrated column density and is the scattering cross section of a two-level atom given by .01 Supplementary Table 1 contains parameters used in the calculation and experiment. The optical density of the cloud is defined such that The atom number density ( , , ) follows a three-dimensional Gaussian distribution where # , ' , ( are the root-mean-square widths of the cloud and * is the peak atom cloud density. We estimate the size of the third dimension (along the imaging axis ) from the geometric mean of the sizes of the other two dimensions ( # = D ' ( ) 10 . The measured OD image can be modeled as where OD O0# = * D 2 ' ( is the peak value of the OD image extracted from the camera which can be used to extract * . The cloud widths are extracted by summing over the raw OD image along each axis and fitting to a one-dimensional Gaussian. The widths in camera pixels are converted to meters based on the measured magnification of the imaging system during which the camera was focused on the MOT cloud fluorescence in steady-state MOT operation. The procedure is repeated for several different time delays between the MOT shut-off and the start of the " pulse corresponding to different values of time-of-flight time ( CDE ). The temperature of the cloud along each axis ' , ( can be determined from the ballistic expansion by plotting the cloud width as a function of CDE , where ',, and (,, are the initial widths of the cloud, P is the Boltzmann constant, and is the mass of a single 87 Rb atom. The total number of atoms is the volume integral of the atom density For images taken at CDE = 0.1 ms, OD O0# = 0.2. We measure = 0.13 ± 0.05 million atoms for a power into the PIC of 65 mW. Note that this power is limited by the total output power of the SOA and therefore explains the lower atom number compared to the peak atom number measured with fluorescence detection. In these calculations the raw OD image from the camera is subject to background and scattered probe light. Any light that is collected by the camera that cannot be absorbed by the cloud will reduce the measured OD. The images are recorded with the Thorlabs DCC3260M CMOS monochrome camera operated with an external voltage trigger.  Comparison of atom number measurements. During absorption imaging TOF measurements the booster optical amplifier (BOA) was used to shutter the optical power input to the beam delivery PIC which outputs a maximum power of 65 mW into the PIC corresponding to an average power per PIC beam of 0.460 mW. We did not optimize for the atom number during the absorption imaging measurements. During the fluorescence measurements a tapered amplifier (TA) was used, allowing for reaching over 180 mW into the PIC. We measured the fluorescence atom number for several input powers into the PIC, corresponding to 1%1 / .01 ∈ (6,20) shown in Supplementary  Figure 7. At input powers into the PIC similar to that of absorption imaging setup, we measure = 0.5 ± 0.1 million atoms. Furthermore, during the absorption imaging the atom number was not continuously optimized. We expect that repump frequency drift, repump power, and cooling laser locking was not optimal. We observe a saturation of the MOT fluorescence power at a repump intensity above 12 mW cm -2 while we can only reach 3 mW cm -2 for peak atom number measurements and 1.5 mW cm -2 for absorption imaging measurements. As the purpose of this work is to demonstrate the PIC-based delivery of all the beams for MOT operation, the limited repump intensity likely limited the achievable atom number for both measurements. In the future we will use a sideband modulator to generate the repump from the cooling laser by applying ~6.8 GHz sidebands. shape B" = 3.45 mm by B& = 2.50 mm. We calculate the beam overlap volume by assuming a rectangular prism with volume = B" B& & = 22 mm 3 . This volume is ~2 times smaller than the volume used for a comparable atom number GMOT as shown in Supplementary Figure 8. Furthermore, these GMOTs utilize an input free-space beam of diameter 20 mm which requires beam expansion and collimation optics. The shaded region denotes the transition region where previous work 12 has identified a change in the scaling of atom number and trapping volume. System integration. Diffraction grating MOTs (GMOTs) have proven to be successful approach in the miniaturization of cold atom systems 15 . However, this technology has limitations in the ability to bring cold atom technology to modular, controllable, and scalable systems. A PIC-based platform offers several key advantages. The Si3N4 beam delivery chip is compatible with chipscale laser integration 16 . Directly butt-coupling an edge-emitting chip-scale laser to the beam delivery PIC obviates the need for fiber-to-chip coupling. This could improve the total efficiency of the cold atom device, which can be defined by comparing the electrical power consumption of the integrated laser to the MOT optical trapping intensity and the atom number. It is possible to extend the system to multiple integrated laser sources and beam emitters as the PIC can be made to support multiple different wavelengths 17,18 . This can be designed to operate in a single silicon nitride thickness (for example 120 nm used in this work) with mask-level changes in the lithography mask.

Supplementary
The PICMOT offers a different configuration for optical access in a chip-scale cold atom system. A comparison of optical access is given in Table 1 of the main text. We consider an atomic vacuum cell in the shape of a rectangular prism and assume that one face of the cell is dedicated to the atomic source and vacuum pump. The four-beam tetrahedral beam configuration of a GMOT places constraints on the optical access for probing and imaging. There are three faces of optical access and the input vertical beam in a GMOT makes it difficult to image a MOT at a nonorthogonal angle 19 . While this can be overcome by machining a central hole in grating chip 20 (hence a fourth face of access), this extends the size of the package that is already limited by the beam expansion optics required for the input beam. On the other hand, the PICMOT allows for four faces of optical access, with an optional fifth face is we consider probe beams emitted by the PIC. This extension of PIC to accommodate other beams, such as probe beams for Raman and two-photon transitions, can be achieved by modifying the lithography mask as described above. Improvements to optical access can also enable collection of a stronger atomic fluorescence signal which may eliminating the need for higher SWaP detectors or complicated imaging schemes 19 .